Jerry has a miniature model of a boat. He knows that the boat is 3 3/4 inches wide and 5 1/2 inches long. What is the actual length of the boat if the actual width is 15 feet?
Width of the miniature model = [tex]3\frac{3}{4}[/tex] inches
Length of the miniature model = [tex]5\frac{1}{2}[/tex] inches
The actual width of the boat = 15 feet
Let us find the actual length of the boat.
Write it in a proportion form.
width of model : length of model : : width of actual : length of actual
[tex]$\Rightarrow 3\frac{3}{4}:5\frac{1}{2}::15:x[/tex]
[tex]$\Rightarrow\frac{15}{4}:\frac{11}{2}::15:x[/tex]
[tex]$\Rightarrow\frac{\frac{15}{4}}{\frac{11}{2}} =\frac{15}{x}[/tex]
Do cross multiplication.
[tex]$\Rightarrow{\frac{15}{4}x =15\times\frac{11}{2}[/tex]
[tex]$\Rightarrow{\frac{15}{4}x =\frac{165}{2}[/tex]
[tex]$\Rightarrow x =\frac{165}{2}\times{\frac{4}{15}[/tex]
⇒ x = 22
Hence the actual length of the boat is 22 feet.
What is the value of 4x 3+4x when x=4
Final answer:
The value of 4x when x=4 is 16, and for proportions like 1:2=4:x, you'd get x=8 by cross multiplying.
Explanation:
The value of 4x when x=4 is simply 4 multiplied by 4, which equals 16. This calculation is a basic algebraic operation, and it should not be confused with more complex problems. For example, if you're trying to solve a proportion like 1:2=4:x, you'd set up a proportion to figure out the value of x. To solve for x you can use the cross multiplication method, resulting in 1x = 8, hence x = 8.
Final answer:
The value of 4x^3 + 4x when x=4 is found by substituting 4 into the expression and simplifying step by step, resulting in a final answer of 272.
Explanation:
When answering a question such as "What is the value of 4x3 + 4x when x=4," we need to substitute the value of x into the expression and simplify.
Let's break it down step-by-step:
Substitute x with 4 into the expression: 4(4)3 + 4(4).
Calculate the exponent: (4)3 = 4 x 4 x 4 = 64.
Multiply by 4: 4 x 64 = 256.
Add the second term: 256 + 4(4).
Perform the second multiplication: 4 x 4 = 16.
Add the two results together: 256 + 16.
Get the final answer: 272.
The value of 4x3 + 4x when x=4 is 272.
carol buys a house for £234900
she pays a 10% deposit
10% of £234900
Carol needs to pay a 10% deposit for a house priced at £234900. Calculating the deposit involves applying a percentage formula, concluding that the deposit will amount to £23490.
Explanation:The subject here is mathematics, and we are dealing with a problem related to percentages. Carol is buying a house for £234900 and needs to pay a 10% deposit. To calculate a percentage, we multiply the total amount by the percentage (in this case, 10%) and divide by 100.
Using this method, we find that 10% of £234900 equals £23490. Therefore, Carol must pay a deposit of £23490 for the house she buys.
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A bakery has 36 glazed donuts on display.This is 80% of the total number of donuts what is the total number of donuts in the bakery
Answer:
45
Step-by-step explanation:
Given:
A bakery has 36 glazed donuts on display.
This is 80% of the total number of donuts.
Question asked:
what is the total number of donuts in the bakery ?
Solution:
Let total number of donuts in the bakery = [tex]x[/tex]
80% of total number of donuts = 36 (given)
[tex]80\% of x = 36[/tex]
[tex]\frac{80x}{100} = 36[/tex]
Multiplying both side by 100
[tex]80x = 3600[/tex]
Dividing both side by 80
[tex]x = 45\\[/tex]
Thus, the number of donuts in the bakery is 45
Tina wants to run 12 3/5 miles over 7 days she wants to run the same distance each day how far must she run each day
To find out how much Tina needs to run each day, divide the total miles she wants to run by the number of days. The result is that Tina needs to run 1.8 miles each day.
Explanation:To find out how far Tina must run each day, we need to divide the total distance she plans to run by the number of days she plans to run. Tina wants to run 12 3/5 miles over 7 days. As a first step, convert her mixed number to an improper fraction. 12 3/5 is equivalent to 63/5.
Now, to find the distance she must run each day, simply divide 63/5 miles by 7 days. Carrying out this division gives us distance of 9/5 miles per day, or in decimal form, 1.8 miles per day.
So, Tina should run 1.8 miles each day to reach her goal.
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I need this asap so if you can help that would be amazing . I can boost the points to more than 50 comment if you want more...
Multiply the number amount of cartridges by the number of books and add that tot he number of cartridges by the number of magazines.:
This needs to be either less than or equal tot he total cartridges she wants to use
40B + 30M ≤ 300
Do the same with pages:
200B + 80M ≤ 1200
12x -3 divided by -5
Answer: 1.8x
Step-by-step explanation:
A car that initially cost 42,000 depreciates in value by approximately 2,000 dollars per year write an equation to represent the value in dollars, Y, of a car X years after it was purchased
Answer:y=42000-2000x
Step-by-step explanation:
Y is price so that’s be 42000 minus 2000 every year
Answer:
[tex]y=42,000 - 2000x[/tex]
Step-by-step explanation:
The y is the total value of the car after everything that needs to be taken account of has been accounted to. You're finding the y and what the price is after x amount of years. The initial amount is 42,000 so whatever the cost of the car has depreciated would be subtracted from it. 2,000 dollars per year means what ever x is for year, let's say 5. The amount of money that the car has depreciated over the course of 5 years would be 5 multiply by 2,000. Hopes this help!
Tickets to a play cost $12.75 per ticket plus a $12.00 fee per order online. At the box office the cost is $15.75 per ticket.
Answer:
[tex]C=12.75n+12.00\\[/tex]
[tex]C= 15.75 n[/tex]
Step-by-step explanation:
When buying tickets to a play online, they cost $12.75 per ticket plus a $12.00 fee per order. When buying tickets at the box office, they cost $15.75 per ticket. The total cost, c, of going to the play, for n people can by represented by a system of equations.
. Write a system of equations that could be used to find how many tickets you have to buy for the cost to be the same.
Let n be the number of people and C be the total cost
Play online
[tex]C=12.75n+12.00\\[/tex]
For Box office
[tex]C= 15.75 n[/tex]
These are the system of equations
To find the cost to be same , make both equations equal to each other and solve for n
The number of tickets bought which will make the online order and box office order equal is 4 tickets
How to write equationn = number of tickets soldCost of online order:
C = 12.75n + 12
Cost of box office order:
C = 15.75n
Equate both equations12.75n + 12 = 15.75n
12 = 15.75n - 12.75n
12 = 3n
n = 12/3
n = 4
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Juan is waiting for the roller coaster at an amusement park. He has been told there is a 40% chance that he will have to wait more than 15 minutes. Find the probability both as a decimal and as a reduced fraction
Answer:
0.4, 2/5
Step-by-step explanation:
The probability that Juan has to wait more than 15 minutes is 0.4 and the probability that Juan doesn't have to wait for more than 15 minutes is 0.6
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, there is a 40% chance that he will have to wait more than 15 minutes. Thus the probability of him waiting for more than 15 minutes is 0.4 and the probability that he has to wait less than 15 minutes is 1-0.4=0.6
Hence, P(<15)=0.6 or 3/5 and P(>15) = 0.4 or 2/5 are the probabilites for Juan
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32h = 288 solve for h
Answer:
h= 9
Step-by-step explanation:
you divide both sides by 32
and 288 divided by 32 is 9
A farmer produces about $3000 eggs each day and sell them for $0.80 per dozen. On average, how much money does the farm get for its eggs each day?
Answer:
$200
Step-by-step explanation:
1. 3000 divided by 12 = 250
2. 250 x 0.80 = 200
i hope i helped
Anybody know the answer I need help. Please
Answer:
[tex]\dfrac{p^2+9p+2}{p^2-49}[/tex]
Step-by-step explanation:
Problems like this require that you recognize that the denominator of the right term is a factor of the denominator of the left term. That is, you're supposed to know how to recognize and factor the difference of two squares.
[tex]\dfrac{5-p}{49-p^2}+\dfrac{p+1}{p-7}=\dfrac{p-5}{p^2-49}+\dfrac{p+1}{p-7}\\\\=\dfrac{p-5}{(p-7)(p+7)}+\dfrac{p+1}{p-7}\cdot\dfrac{p+7}{p+7}\\\\=\dfrac{(p-5)+(p+1)(p+7)}{(p-7)(p+7)}=\dfrac{p-5+p^2+8p+7}{p^2-49}=\dfrac{p^2+9p+2}{p^2-49}[/tex]
Which value is NOT equivalent to the other values? 1/25 0.04 4% 0.4
Let's convert them to decimals:
1/25 = 0.04
4% = 0.04
0.04 = 0.04
0.4 = 0.40.
So 0.4 is NOT equivalent to the other values.
The values 1/25, 0.04, and 4% are all equivalent to each other. The value that does not match with these is 0.4.
Explanation:The values given in the question are 1/25, 0.04, 4%, and 0.4. These values can be converted into the same format to compare them more easily.
Firstly, you can convert 1/25 into a decimal, which equals 0.04. Secondly, we can convert 4% into a decimal by dividing the number 4 by 100, which also equals 0.04. Lastly, when comparing these to 0.4, it becomes clear that 0.4 is not equivalent to the other numbers (0.04).
So, the value which is not equivalent to the others is 0.4.
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The measure of <B is (3x - 4) and the measure of
<D is (2x-6)”. What are the measures of angles B
and D?
m<B=
m<D =
Step-by-step explanation:
Given information is insufficient for finding the measures of angles B and D.
Answer:
110 and 70
Step-by-step explanation:
what is 489+ 9860 TELL ME SLAVES
Answer:10,349
Step-by-step explanation:
y = A system of equations. y equals StartFraction one-half EndFraction x minus 6. x equals negative 4.x – 6
x = –4
What is the solution to the system of equations?
(–8, –4)
(–4, –8)
(–4, 4)
(4, –4)
Answer:
(-4,-8) is the answer
on ed 2021 :)
hope this helps!!!!!
I have to round 312016.29 to the nearest whole number what would I do??
Answer:
312016 is your correct answer
Step-by-step explanation:
For the function defined by f(x)=12/x^2, what is the constant proportionality
A. 120
B.undefined
C. 12
D.1200
Answer:
12
Step-by-step explanation:
Find the equation of the line in gradient intercept for that has an x intercept of 3 and a y intercept of -4. Show working out
Answer:
y = (4/3)x - 4
Step-by-step explanation:
(3,0) & (0,-4)
m = (-4-0)/(0-3) = -4/-3 = 4/3
y = (4/3)x + c
c is the y-intercept which is -4
y = (4/3)x - 4
What is 28.93 in expanded form
Answer:20+8+.9+.03
Step-by-step explanation:
Final answer:
The number 28.93 in expanded form is written as 20 + 8 + 0.9 + 0.03.
Explanation:
The number 28.93 in expanded form is written as 20 + 8 + 0.9 + 0.03. To expand a decimal number, we break it down into its place values, where each digit is represented by its value in terms of tens, ones, tenths, hundredths, and so forth. In the case of 28.93, the '2' is in the tens place and represents 20, the '8' is in the ones place and represents 8, the '9' is in the tenths place and represents 0.9, and the '3' is in the hundredths place and represents 0.03.
mira's kitchen holds up to 103.468 liters of water. round this amount to the nearest liter WORTH: 10 PTS
Answer:
It would round down to 103 liters.
Step-by-step explanation:
-WILL GIVE BRAINLY- Write an equivalent expression using the distributive property. a. 12x + 10 b. – x + 8
Answer:
Step-by-step explanation:
A) 12x+10=2(6x+5)
B) -x+8=-(x-8)
What is the midpoint of the segment of the segment that would be created between points L and N on a graph?
Option A:
Midpoint of LN = (2, 3)
Solution:
In the given graph we can find the coordinates of L and N.
Coordinates of L = (–2, 3)
Coordinates of N = (6, 3)
Here, [tex]x_{1}=-2, x_{2}=6, y_{1}=3, y_{2}=3[/tex]
Let us find the midpoint of the segment LN.
Midpoint formula:
[tex]$\text { Midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
[tex]\begin{aligned}&=\left(\frac{-2+6}{2}, \frac{3+3}{2}\right)\\&=\left(\frac{4}{2}, \frac{6}{2}\right)\\&=(2,3)\end{aligned}[/tex]
Midpoint of LN = (2, 3)
Option A is the correct answer.
Hence the coordinates of the midpoint of the line segment LN is (2, 3).
c) Find the value of x:
5x + 2 = 4x + 8
Which are true of the function f(x)=49(1/7)^x
select three options.
1) the domain is the set of all real numbers
2) the range is the set of all real numbers
3) the domain is x>0
4) the range is y>0
5) as x increased by 1, each y-value is one seventh of the previous y-value
The Option (1),(4) and (5) are correct.
Step-by-step explanation:
The function given to us is : y= f(x) =49(1/7)^x
The following statements are true regarding the above function is
As you can see that the value of y(49)is defined for all values of x , so the Domain is the set of all values of x , which is set of all real numbers.X is defined for all values of y. So the Range of all the values that y can take is also set of all real numbers greater than zero, i.e y>0.As x increased by 1, each y-value is one seventh of the previous y-valueAnswer:
The correct options are 1, 4 and 5.
Step-by-step explanation:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is initial value and b is growth factor.
Domain of this function is all real numbers. If a>0, then range is all positive numbers.
The given function is
[tex]f(x)=49(\frac{1}{7})^x[/tex]
where, a =49 and b=1/7.
It is an exponential function. So, the domain is the set of all real numbers.
Since, a=49 which is a positive value, therefore the range is y>0.
The value of b is 1/7, it means as x increased by 1, each y-value is one seventh of the previous y-value.
Therefore, the correct options are 1, 4 and 5.
Please solve the following system of equations by
substitution.
y = 3x - 4 and 4x + 3y = 1
Answer:
(1 , -1)Step-by-step explanation:
y = 3x - 4 (1)
4x + 3y = 1 (2)
if we substitute y by 3x - 4 in the second equation we get
4x + 3(3x-4) = 1 ⇒ 4x + 9x - 12 = 1 ⇒ 13x = 13 ⇒ x = 1
now ,we substitute x by 1 in the first equation
y = 3(1) - 4 = 3 - 4 = -1
4a-5b:5a+4b=1:3 then find the value of a:b
Answer:
a : b = 19 : 7
Step-by-step explanation:
Given
4a - 5b : 5a + 4b = 1 : 3
Expressing in fractional form, that is
[tex]\frac{4a-5b}{5a+4b}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )
3(4a - 5b) = 5a + 4b ← distribute left side
12a - 15b = 5a + 4b ( subtract 5a from both sides )
7a - 15b = 4b ( add 15b to both sides )
7a = 19b ( divide both sides by 7 )
a = [tex]\frac{19}{7}[/tex] b ( divide both sides by b )
[tex]\frac{a}{b}[/tex] = [tex]\frac{19}{7}[/tex]
That is a : b = 19 : 7
Answer:
Step-by-step explanation:
4a-5b:5a+4b=1:3
4a-5b/5a+4b=1:3cross multiply
3(4a-5b)=1(5a+4b)
12a-15b=5a+4b
Collect like terms
12a-5a=4b+15b
7a=19b
a:b=7:19
When a=2 b=3 and c=5 what is the value of a(b+c)
Show how you got the answer
Answer:
B =
Step-by-step explanation:B + C would be 8 because B=2 and C=5. 5 + 8 is 8
A farmer has two pieces of land in a parallelogram shape on the same base. He grows vegetables and flowers in two triangular pieces of land as shown in diagram.
Q: Check whether the two triangular pieces of land are equal in area.
Step-by-step explanation:
In trapezoid ABCF, AB || CF.
Therefore, parallelograms ABEF & ABCD have same height and lie on the same base AB.
[tex] \therefore Ar(\parallel^{gm} ABEF) = Ar(\parallel^{gm}ABCD)\\... (1)\\\\
\because\: Ar(\parallel^{gm} ABEF) \\=Ar(\triangle AFD) + Ar(\square \: ABED)....(2) \\\\
\&\: Ar(\parallel^{gm}ABCD)\\= Ar(\triangle BCE) +Ar(\square ABED)....(3) [/tex]
From equations (1), (2) & (3), we find:
[tex] Ar(\triangle AFD) + Ar(\square \: ABED) \\ = Ar(\triangle BCE) +Ar(\square ABED)
\\ \\ \purple {\boxed {\therefore Ar(\triangle AFD) = Ar(\triangle BCE)}}
\\ [/tex]
Thus, the two triangular pieces of land are equal in area.
Hence proved.